How The Mind Creates Mathematics

Stanislas Dehaene



    Part I. Our Numerical Heritage

    Chapter 1. Talented and Gifted Animals
      A Horse Named Hans
      Rat Accountants
      How Abstract Are Animal Calculations?
      The Accumulator Metaphor
      Number-Detecting Neurons?
      Fuzzy Counting
      The Limits of Animal Mathematics
      From Animal to Human
    Chapter 2. Babies Who Count
      Baby Building: Piaget's Theory
      Piaget's Errors
      Younger and Younger
      Babies' Power of Abstraction
      How Much Is 1 plus 1?
      The Limits of Infant Arithmetic
      Nature, Nurture, and Number
    Chapter 3. The Adult Number Line
      1, 2, 3, and Beyond
      Approximating Large Numbers
      The Quantity Behind the Symbols
      The Mental Compression of Large Numbers
      Reflexive Access to Number Meaning
      A Sense of Space
      Do Numbers Have Colors?
      Intuitions of Number

    Part II. Beyond Approximation

    Chapter 4. The Language of Numbers
      A Short History of Number
      Keeping a Permanent Trace of Numerals
      The Place - Value Principle
      An Exuberant Diversity of Number Languages
      The Cost of Speaking English
      Learning to Label Quantities
      Round Numbers, Sharp Numbers
      Why Are Some Numerals More Frequent Than Others?
      Cerebral Constraints on Cultural Evolution
    Chapter 5. Small Heads for Big Calculations
      Counting: The ABC of Calculation
      Preschoolers as Algorithm Designers
      Memory Appears on the Scene
      The Multiplication Table: An Unnatural Practice?
      Verbal Memory to the Rescue
      Mental Bugs
      Pros and Cons of the Electronic Calculator
      Innumeracy: Clear and Present Danger?
      Teaching Number Sense
    Chapter 6. Geniuses and Prodigies
      A Numerical Bestiary
      The Landscape of Numbers
      Phrenology and the Search for Biological Bases of Genius
      Is Mathematical Talent a Biological Gift?
      When Passion Produces Talent
      Ordinary Parameters for Extraordinary Calculators
      Recipes for Lightning Calculation
      Talent and Mathematical Invention

    Part III. Of Neurons and Numbers

    Chapter 7. Losing Number Sense
      Mr. N, the Approximate Man
      A Clear-Cut Deficit
      A Champion in Numerical Non-sense
      Inferior Parietal Cortex and the Number Sense
      Seizures Induced by Mathematics
      The Multiple Meanings of Numbers
      The Brain's Numerical Information Highways
      Who Orchestrates the Brain's Computations?
      At the Origins of Cerebral Specialization
    Chapter 8. The Computing Brain
      Does Mental Calculation Increase Brain Metabolism?
      The Principle of Positron Emission Tomography
      Can One Localize Mathematical Thought?
      When the Brain Multiplies or Compares
      The Limits of Positron Emission Tomography
      The Brain Electric
      The Time Line of the Number Line
      Understanding the Word "Eighteen"
      Numerate Neurons
    Chapter 9. What Is a Number?
      Is the Brain a Logical Machine?
      Analog Computations in the Brain
      When Intuition Outruns Axioms
      Platonists, Formalists, and Intuitionists
      The Construction and Selection of Mathematics
      The Unreasonable Effectiveness of Mathematics
Notes and References


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